Question: Determine the intercepts of the line. $ y+1=3(x-4)$ $x$ -intercept: $\Big($
Solution: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}+1&=3(x-4)\\ 1&=3x-12\\ 13&=3x\\ \dfrac{13}{3}&=x\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{13}{3},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y+1&=3({0}-4)\\ y+1&=-12\\ y&=-13\end{aligned}$ So the $y$ -intercept is $\left(0,-13\right)$. In conclusion, The $x$ -intercept is $\left(\dfrac{13}{3},0\right)$. The $y$ -intercept is $\left(0,-13\right)$.